Annals of Operations Research

, Volume 20, Issue 1, pp 67–96

The auction algorithm for the transportation problem

  • Dimitri P. Bertsekas
  • David A. Castanon

DOI: 10.1007/BF02216923

Cite this article as:
Bertsekas, D.P. & Castanon, D.A. Ann Oper Res (1989) 20: 67. doi:10.1007/BF02216923


The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1989

Authors and Affiliations

  • Dimitri P. Bertsekas
    • 1
  • David A. Castanon
    • 2
  1. 1.Laboratory for Information and Decision SystemsM.I.T.CambridgeUSA
  2. 2.Alphatech, Inc.BurlingtonUSA